Hi Toby! Sorry to hear that your vinyl soft top is deteriorating! Hopefully I can shed some light on why this may have happened!
In my experience, after a period of about 2 years, lower quality vinyl/PVC that has been inappropriately cleaned will begin to breakdown/deteriorate and the plasticiser used during the manufacturing process will begin to leach out. This chemical reaction within the vinyl/PVC will cause the plasticiser to migrate to the surface and cause stickiness.
The stickiness is classically more apparent during warmer periods of the day and will diminish or disappear totally during colder periods or overnight. This is similar to tarmac roads, they are often sticky on warm days but will return to their usual constituency when the ambient temperature is cooler.
If you have not owned your car from new, then you presumably don’t know what has been previously used to clean the soft top prior to your ownership commencing. Car shampoo is not suitable for washing a vinyl soft top, neither are stronger proprietary products such as Cif, the use of these chemicals will accelerate the deteriorating process of the vinyl.